Hypothesis Testing and P Value

BY DR ZAHID KHAN

SENIOR LECTURER KING FAISAL UNIVERSITY, KSA

Two ways to learn about a population

Confidence intervals Hypothesis testing

HYPOTHESIS

What do you mean by a Hypothesis?

A hypothesis is a proposition that is –

assumed as a premise in an argument / claim

set forth as an explanation for the occurrence of some

specified group of phenomena

A hypothesis is a prediction about the outcome of an

experiment. In market research this could be the result of

the out come of a focus or field study

Why do we make hypotheses?

The practice of science traditionally involves formulating and testing hypotheses

Hypotheses are assertions that are capable of being proven false using a test of observed data

Hypothesis testing is a procedure through which sample data is used to evaluate the credibility of a hypothesis

Null Hypothesis The null hypothesis typically corresponds to a general

or default position Making this assertion will make no difference and

hence cannot be proven positively

Alternate Hypothesis An alternate hypothesis asserts a rival relationship

between the phenomena measured by the null hypothesis

It need not be a logical negation of the null hypothesis as it only helps in rejecting or not rejecting the null hypothesis

TYPES OF HYPOTHESIS

Shoppers in a store playing music shop spend more.

Independent Variable: Music in the store

Dependent Variable: Amount spent in store

Dependant and independent variables

1. Obtain a random sample of shoppers who go to stores with music

2. Check shop spending

3. Compare sample data to hypothesis

4. Make decision:1. Reject the hypothesis

2. Fail to reject the hypothesis

Example -- Continued

What are errors in Hypothesis Testing?

The purpose of Hypothesis Testing is to reject or not reject the Null Hypothesis based on statistical evidence

Hypothesis Testing is said to have resulted in an error when the decision regarding treatment of the Null Hypothesis is wrong

TYPES OF ERRORS

TYPES OF ERRORS

Actual State of Affairs

Belief Decision H0 is True H0 is False

H0 is False Reject H0 Type I ErrorFalse Positive

Correct Rejection1 - Power

H0 is True Fail to Reject H0 Correct Failure to Reject1 -

Type II ErrorFalse Negative

1. Probability that the test will correctly reject a false null hypothesis.

2. When a treatment effect exists

1. A study may fail to discover it (Type II error, fail to reject a false null hypothesis)

2. A study may discover it (reject a false null hypothesis)

Statistical Power

During the Hypothesis Testing,α – is the probability of occurrence of a Type-I Error

β – is the probability of occurrence of a Type-II Error

Relationship between α and β For a fixed sample size, the lower we set value of α,

the higher is the value of β and vice-versa In many cases, it is difficult or almost impossible to

calculate the value of β and hence we usually set only α

α, β AND THE INTER-RELATIONSHIP

Interpreting the weight of evidence against the Null Hypothesis for rejecting / not rejecting Ho

If the p-value for testing Ho is less than –

< 0.05, we have strong evidence that Ho is false

< 0.01, we have very strong evidence that Ho is false

< 0.001, we have extremely strong evidence that Ho is false

P value is taken as 0.05 or 5% because it is a standard icon & it

nearly corresponds to the difference of two standard errors.

INTERPRETING RESULTS

Jury’s Decision

Did Not Commit Crime Committed Crime

Guilty Type I ErrorConvict Innocent Person

Correct VerdictConvict Guilty Person

Not Guilty Correct AcquittalFail to Convict Innocent Person

Type II ErrorFail to Convict Guilty Person

1. Alpha: probability of committing a Type I error

1. Reject H0 although it is true

2. Symbolized by

2. Obtained result attributed to:1. Real effect (reject H0)

2. Chance

Level of Significance

One Sided & Two Sided Tests

Consider two means A & B.

One sided test only tells you that A > B.

Two sided tests tells you that either A>B or A <B so leaving you with two options.

Mostly Two sided tests are used except in cases of equivalence tests like Lumpectomy done for Breast surgery as well as radical Mastectomy.

One sided test would be whether Lumpectomy is worst for survival than Radical Mastectomy and we don't bother about better survival results.

Any Questions !!!!

Thank You.